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The next three problems refer to the following situation: Suppose that a sample of 15 randomly chosen people were put on a special weight loss diet. The amount of weight lost, in pounds, follows an unknown distribution with mean equal to 12 pounds and standard deviation equal to 3 pounds.

Exercise 1

To find the probability that the average of the 15 people lose no more than 14 pounds, the random variable should be:

  • A. The number of people who lost weight on the special weight loss diet
  • B. The number of people who were on the diet
  • C. The average amount of weight lost by 15 people on the special weight loss diet
  • D. The total amount of weight lost by 15 people on the special weight loss diet

Solution

C

Exercise 2

Find the probability asked for in the previous problem.

Solution

0.9951

Exercise 3

Find the 90th percentile for the average amount of weight lost by 15 people.

Solution

12.99

The next five problems refer to the following study: Twenty percent of the students at a local community college live in within five miles of the campus. Thirty percent of the students at the same community college receive some kind of financial aid. Of those who live within five miles of the campus, 75% receive some kind of financial aid.

Exercise 4

Find the probability that a randomly chosen student at the local community college does not live within five miles of the campus.

  • A. 80%
  • B. 20%
  • C. 30%
  • D. Cannot be determined

Solution

A

Exercise 5

Find the probability that a randomly chosen student at the local community college lives within five miles of the campus or receives some kind of financial aid.

  • A. 50%
  • B. 35%
  • C. 27.5%
  • D. 75%

Solution

B

Exercise 6

Based upon the above information, are living in student housing within five miles of the campus and receiving some kind of financial aid mutually exclusive?

  • A. Yes
  • B. No
  • C. Cannot be determined

Solution

B

Exercise 7

The interest rate charged on the financial aid is _______ data.

  • A. quantitative discrete
  • B. quantitative continuous
  • C. qualitative discrete
  • D. qualitative

Solution

B

Exercise 8

What follows is information about the students who receive financial aid at the local community college.

  • 1st quartile = $250
  • 2nd quartile = $700
  • 3rd quartile = $1200

(These amounts are for the school year.) If a sample of 200 students is taken, how many are expected to receive $250 or more?

  • A. 50
  • B. 250
  • C. 150
  • D. Cannot be determined

Solution

  • C. 150

The next two problems refer to the following information: P ( A ) = 0 . 2 P ( A ) = 0 . 2 size 12{P \( A \) =0 "." 2} {} , P ( B ) = 0 . 3 P ( B ) = 0 . 3 size 12{P \( B \) =0 "." 3} {} , A A size 12{A} {} and B B size 12{B} {} are independent events.

Exercise 9

P(AANDB)=P(AANDB)= size 12{P \( A} {}

  • A. 0.5
  • B. 0.6
  • C. 0
  • D. 0.06

Solution

D

Exercise 10

P(AORB)=P(AORB)= size 12{P \( A} {}

  • A. 0.56
  • B. 0.5
  • C. 0.44
  • D. 1

Solution

C

Exercise 11

If H H size 12{H} {} and D D size 12{D} {} are mutually exclusive events, {} P ( H ) = 0 . 25 P ( H ) = 0 . 25 size 12{P \( H \) =0 "." "25"} {} , P ( D ) = 0 . 15 P ( D ) = 0 . 15 size 12{P \( D \) =0 "." "15"} {} , then P(H| D )P(H| D ) size 12{P \( H} {}

  • A. 1
  • B. 0
  • C. 0.40
  • D. 0.0375

Solution

B

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